Ebook: An Introduction to Copulas

Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.

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Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.
Content:
Front Matter....Pages N2-xi
Introduction....Pages 1-4
Definitions and Basic Properties....Pages 5-44
Methods of Constructing Copulas....Pages 45-87
Archimedean Copulas....Pages 89-124
Dependence....Pages 125-182
Additional Topics....Pages 183-199
Back Matter....Pages 201-218

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Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.
Content:
Front Matter....Pages N2-xi
Introduction....Pages 1-4
Definitions and Basic Properties....Pages 5-44
Methods of Constructing Copulas....Pages 45-87
Archimedean Copulas....Pages 89-124
Dependence....Pages 125-182
Additional Topics....Pages 183-199
Back Matter....Pages 201-218
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